%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : LCL096-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:14:03 PM UTC 2026
% Result : Unsatisfiable 40.53s 40.84s
% Output : CNFRefutation 40.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 3 RR)
% Number of literals : 35 ( 34 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 116 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) != true,
file('theBenchmark.p',prove_lg_1) ).
cnf(c1,axiom,
ifeq(X,X,Y,Z) = Y,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c2,axiom,
ifeq(is_a_theorem(equivalent(X,Y)),true,ifeq(is_a_theorem(X),true,is_a_theorem(Y),true),true) = true,
file('theBenchmark.p',condensed_detachment) ).
cnf(c3,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),W),W)) = true,
file('theBenchmark.p',lg_2) ).
cnf(c4,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),W)),true,is_a_theorem(W),true) = true,
inference(equational,[status(thm)],[c1,c2,c3]) ).
cnf(c6,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),Z),W),equivalent(equivalent(equivalent(X,V),Z),equivalent(equivalent(Y,V),W)))) = true,
file('theBenchmark.p',lg_4) ).
cnf(c7,plain,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(equivalent(W,Y),equivalent(W,Z)))) = true,
inference(equational,[status(thm)],[c1,c4,c6]) ).
cnf(c8,plain,
ifeq(is_a_theorem(equivalent(equivalent(X,Y),equivalent(X,Z))),true,is_a_theorem(equivalent(equivalent(W,Y),equivalent(W,Z))),true) = true,
inference(equational,[status(thm)],[c1,c2,c7]) ).
cnf(c9,plain,
is_a_theorem(equivalent(equivalent(X,equivalent(Y,Z)),equivalent(X,equivalent(Y,Z)))) = true,
inference(equational,[status(thm)],[c1,c7,c8]) ).
cnf(c10,plain,
is_a_theorem(equivalent(equivalent(X,Y),equivalent(X,equivalent(equivalent(Z,Z),Y)))) = true,
inference(equational,[status(thm)],[c1,c6,c8]) ).
cnf(c11,plain,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z))) = true,
inference(equational,[status(thm)],[c1,c4,c9]) ).
cnf(c14,plain,
ifeq(is_a_theorem(equivalent(equivalent(X,Y),equivalent(X,Z))),true,is_a_theorem(equivalent(Y,Z)),true) = true,
inference(equational,[status(thm)],[c1,c2,c11]) ).
cnf(c15,plain,
is_a_theorem(equivalent(X,equivalent(equivalent(Y,Y),X))) = true,
inference(equational,[status(thm)],[c1,c10,c14]) ).
cnf(c34,plain,
is_a_theorem(equivalent(equivalent(X,X),equivalent(equivalent(equivalent(Y,Z),equivalent(Y,W)),equivalent(Z,W)))) = true,
inference(equational,[status(thm)],[c1,c4,c15]) ).
cnf(c37,plain,
is_a_theorem(equivalent(equivalent(X,equivalent(equivalent(Y,Z),equivalent(Y,W))),equivalent(X,equivalent(Z,W)))) = true,
inference(equational,[status(thm)],[c1,c8,c34]) ).
cnf(c54,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,equivalent(equivalent(Z,Z),Y))),W)),true,is_a_theorem(W),true) = true,
inference(equational,[status(thm)],[c1,c2,c10]) ).
cnf(c55,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,X),Y),Z),equivalent(Y,Z))) = true,
inference(equational,[status(thm)],[c1,c37,c54]) ).
cnf(c56,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X,X),Y),Z)),true,is_a_theorem(equivalent(Y,Z)),true) = true,
inference(equational,[status(thm)],[c1,c2,c55]) ).
cnf(c113,plain,
ifeq(is_a_theorem(equivalent(equivalent(equivalent(X,Y),Z),W)),true,is_a_theorem(equivalent(equivalent(equivalent(X,V),Z),equivalent(equivalent(Y,V),W))),true) = true,
inference(equational,[status(thm)],[c1,c2,c6]) ).
cnf(c114,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),W),V),equivalent(equivalent(equivalent(Y,Z),W),V))) = true,
inference(equational,[status(thm)],[c1,c3,c113]) ).
cnf(c115,plain,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),W)),equivalent(equivalent(Z,Y),W))) = true,
inference(equational,[status(thm)],[c1,c4,c114]) ).
cnf(c117,plain,
is_a_theorem(equivalent(equivalent(X,equivalent(equivalent(Y,Y),Z)),equivalent(X,Z))) = true,
inference(equational,[status(thm)],[c1,c8,c115]) ).
cnf(c122,plain,
ifeq(is_a_theorem(equivalent(X,equivalent(equivalent(Y,Y),Z))),true,is_a_theorem(equivalent(X,Z)),true) = true,
inference(equational,[status(thm)],[c1,c2,c117]) ).
cnf(c124,plain,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(Y,X),Z)),Z)) = true,
inference(equational,[status(thm)],[c1,c115,c122]) ).
cnf(c149,plain,
is_a_theorem(equivalent(equivalent(X,equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),W))),equivalent(X,W))) = true,
inference(equational,[status(thm)],[c1,c8,c124]) ).
cnf(c179,plain,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(equivalent(W,Y),equivalent(equivalent(V,W),equivalent(V,Z))))) = true,
inference(equational,[status(thm)],[c1,c7,c113]) ).
cnf(c234,plain,
is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,X),equivalent(equivalent(W,Z),equivalent(W,Y))))) = true,
inference(equational,[status(thm)],[c1,c56,c179]) ).
cnf(c346,plain,
is_a_theorem(equivalent(X,equivalent(equivalent(Y,equivalent(Z,Z)),equivalent(equivalent(W,Y),equivalent(W,X))))) = true,
inference(equational,[status(thm)],[c1,c56,c234]) ).
cnf(c378,plain,
ifeq(is_a_theorem(equivalent(X,equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),W)))),true,is_a_theorem(equivalent(X,W)),true) = true,
inference(equational,[status(thm)],[c1,c2,c149]) ).
cnf(c472,plain,
is_a_theorem(equivalent(X,equivalent(equivalent(Y,Z),equivalent(Y,equivalent(equivalent(Z,equivalent(W,W)),X))))) = true,
inference(equational,[status(thm)],[c1,c14,c346]) ).
cnf(c852,plain,
is_a_theorem(equivalent(X,equivalent(Y,equivalent(equivalent(Z,equivalent(W,W)),equivalent(equivalent(Y,Z),X))))) = true,
inference(equational,[status(thm)],[c1,c14,c472]) ).
cnf(c853,plain,
is_a_theorem(equivalent(X,equivalent(equivalent(equivalent(equivalent(Y,Y),Z),Z),X))) = true,
inference(equational,[status(thm)],[c1,c378,c852]) ).
cnf(c854,plain,
is_a_theorem(equivalent(equivalent(equivalent(X,equivalent(equivalent(Y,Y),X)),Z),Z)) = true,
inference(equational,[status(thm)],[c1,c378,c853]) ).
cnf(g1,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) = true,
inference(equational,[status(thm)],[c854]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL096-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : run_Leo-III %s %d THM
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 4 13:20:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 40.53/40.84 % SZS status Unsatisfiable
% 40.53/40.84 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------